The land of the Plymouth Colony was not commonly held by some nebulous public system but by a joint stock system between a group of investors and the Crown, with the Crowns major investment being a royal writ for the territory claimed by the colony being held being the property of the Colonists according to English Common law.

As for the initial failures of the Plymouth Colony, one should probably blame the colonists attempts to use Old World plants in New England, a much colder climate, as well as their initial profound refusal to eat the local food, up to and including capturing oysters and lobsters to feed their diminishing stock of pigs. This poor planning and ignorance can probably be accredited to the fact that the ships manifest for the initial Plymouth landing lists NO farmers or productive tradesmen as passengers. This is probably why a third to half of the colonists died the first winter. And the purchase of the land by the individual colonists from the joint stock company over time didn't improve the situation.

The only reason the Plymouth colony succeeded, like most of the New England colonies the British established, was that eventually immigration from England outweighed deaths and emigration back to England by enough that the population stabilized and the colony was able to develop a functioning system of commerce. Why did this happen? Because eventually the system of replacement was overwhelmed by people eager to join in on the new and lucrative tobacco and fur trades. The Plymouth colony became part of this larger economy, and survived. Not all of the starter colonies did. Socialism or capitalism has nothing to do with it. Especially considering that no Englishmen of note was a real capitalist at the time of the Plymouth landing, all of them instead subscribing to mercantilism, which has no firm position on collective or individual land ownership.

Now, even if the Plymouth Colony had been a socialist experiment, it would say nothing about the viability of socialism, just as the sinking of the Titanic or the bankruptcy of Enron say nothing about the viability of capitalism.